# How to Make a Lee's Disk for Measuring Thermal Conductivity

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## Introduction: How to Make a Lee's Disk for Measuring Thermal Conductivity

INTRODUCTION
Lee’s Disc is a simple and effective method to calculate the thermal conductivities of insulative materials. Little is known about the origins of Lee and Chorlton’s method to determine thermal conductivity, but the earliest mention of their work can be found in the 41st Volume of the Philosophical Magazine (1896)1. Anyone can operate and assemble a Lee’s Disc apparatus, as most of the components are affordable, and can be found on any general online retailer or hardware store. Ultimately, Lee’s Disc is an easy at-home method that allows users to understand how to calculate thermal conductivity.

MATERIALS

Amazon.com or similar online retailers carry most of the materials required for this application.

• Brass disc (2″ x 0.5″=50 mm x 13 mm) x2
• Lab stands
• Vernier caliper
• Ring clamp (minimum 2″=50 mm)
• Cord (32″-4′=820-1200 mm)
• BalanceThermometers x2
• Bolts x4 (bolt diameter smaller than 1/2 the width of the brass disc)
• Insulating material (cotton, felt, plastic)
• Thermal grease

The following materials are also required to manufacture Lee’s Disc, however it is possible to build them at home for a fraction of the price. If you are interested in building any or all of the following components, please refer to the final segment of this post.

• Steam generator
• Steam chamber
• Two channel thermocouples (optional)

## Step 1: Assembling Lee's Disc

1. Machine 4 holes into the side of one of the brass discs, separated by ¼ of the circumference. This will become the lower suspended disc.
2. Insert 1 bolt into each hole.
3. Cut the cord into 4 equal lengths, and tie each section around the protruding end of the 4 bolts.
4. Machine 1 hole that is slightly larger than the diameter of the thermometer (or thermocouple) into the side of each brass disc.
5. Fill the hole with thermal grease to prevent air pockets from forming, then insert the thermometer (or thermocouple).

## Step 2: Experimental Set-Up

1. Set-up the lab stand, placing the ring clamp just below the top of the stand.
2. Secure the 4 cords that are attached to the lower brass disc to the ring clamp.
3. Use the Vernier caliper to measure the thickness (OR mean thickness) of the sample and record this as the distance that the heat is to be transferred (d).
4. Place the sample material on the lower suspended brass disk, then position the upper brass disc on top of the sample.
5. Finally, rest the steam chamber on the upper brass disc.

## Step 3: Procedure

1. Turn on the steam generator.
2. Allow the entire system to reach steady-state (no change in temperature by more than 0.5 degrees in 10 minutes).
3. Once steady state is reached, record the temperature displayed on each thermometer in the upper and lower brass discs (T1 and T2, respectively), then remove the sample material from the apparatus.
4. Place the steam chamber and the upper brass disc on top of the lower brass disc, and allow the system's temperature to rise by 10-15 °C above steady-state (T2).
5. Once this temperature has been achieved, remove the steam chamber and the upper brass disc from the apparatus and turn off the steam generator.
6. Quickly place an insulating material on top of the lower brass disc, making sure to cover the area that was occupied by the steam chamber.
7. Record the temperatures within ±5°C of T2 at regular time intervals (5-10 seconds), as the lower brass disc cools and approaches T2.

## Step 4: Calculating Thermal Conductivity

1. Plot a Temperature vs. Time graph by hand or use any available program (such as excel).
2. On the lower brass disc cooling curve, calculate the slope of the tangent line to T2 by hand or with computer software.

The following equation can be used to find the rate of heat transfer through a material at steady state:

Q = k ⋅ A ⋅ (T1– T2)/d

Whereas, the rate ofheat loss in a steady state system is represented by the following equation:

Q = m · c · (dT/dt)

However, because the system is at steady state, the amount of heat entering and leaving the system is the same. Therefore, the previous two equations can be set equal to one another:

k ⋅ A ⋅ (T1– T2)/d = m ⋅ c ⋅ (dT/dt)

Where:

• k = thermal conductivity in Watts/meter·Kelvin (W/mK)
• A = area in meter squared (m2)
• T1, T2 = temperature of the upper and lower brass discs (respectively) in Kelvin (K)
• d = distance that the heat travels in meters (m)
• m = mass of a given sample in kilograms (kg)
• c = specific heat of a given material in Joules/kilogram·Kelvin (J/kgK)
• (dT/dt) = rate of cooling in Kelvin/second (K/s)

The thermal conductivity of the system can then be found by isolating 'k', which yields the following equation:

k = [m ⋅ c ⋅ (dT/dt) ⋅ d]/A ⋅ (T1– T2)

## Step 5: Verification

Once the thermal conductivity of the sample has been calculated, the results can be compared to data obtained from highly specialized labs, as seen in the following table.

Type of MaterialThermal Conductivity Constant (W/m-k) Gmanila Wood0.0914 Rubber0.1720 Oak Wood0.1850 Nylon0.2300 Asbestos Cement Sheet0.3190 Varried PVC0.04 - 0.350

*Thermal Conductivity values taken from the Thermtest thermal properties database, for more Thermal Conductivity values visit: https://www.thermtest.com/materials-database

Conclusion

Opposite to the Searle’s Bar experiment, Lee’s Disc method is designed to primarily calculate the thermal conductivities of thermal insulators, such as polystyrene. Thin samples with large surface areas are preferable for this application, because they quickly reach steady state. With a budget between 150-250\$, anyone can easily test the thermal conductivity of insulating materials.

Web Resources for further information:
/thermal-resources/build-your-own/searles-apparatus
/history-6-lees-disc-method/
http://iosrjournals.org/iosr-jmce/papers/vol3-issue1/F0315360.pdf?id=2586

To make your own simulation:
/thermal-resources/energy2d-heat-transfer-simulations/

Reference

Lees CH, Chorlton JD. 1896. On a Simple apparatus for determining the thermal conductivity of cements and other substances used in the Arts. Philosophical Magazine. 41:253.

How to Save a Few Extra Dollars

For those who are more tech savvy, the following components of this experiment can be made at home for a fraction of the price.

Steam Chamber

Materials

• Thin walled metal cylinder
• High thermal conductivity (ex: aluminum, copper).
• Height must be less than the available area between the upper brass disc and the ring clamp.
• Must cover the cross-sectional area of the upper brass disc, where cross-sectional area = πD2/4 OR πr2

Procedure

Machine 1 hole on each side of the cylinder for the steam inlet and outlet.

Steam Generator

Materials

• Hot plate
• Closed metal container filled with water
• Must have an air tight lid with a hole large enough for tubing.

Procedure

Connect the tubing with the steam inlet hole of the steam chamber. It is important to note that the airtight seal will produce a closed system, and pressure could build if the tubing is faulty.

Two Channel Thermocouple

The above image is an appropriate design of a two channel thermocouple that is capable of auto-recording temperature.

ADC chips like ADS1248 and MCP3424 can read the temperatures of the metal plates supplied by the thermocouples; the digital value of which would be sent to a CPU such as ARM cortex o. The CPU can record the temperatures and time which would then be displayed, stored, or sent to a computer. Keep in mind that the thermocouples need cold joint compensation. This can be completed by a thermistor or IC temperature sensor, like DS18B20, at the thermocouples’ cold joint.

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